Most trains will be running. Delft, the Hague, and Cologne will not be a problem. You can check specific schedules at:
Schedules for late december are not yet available. Check them in September, but you won't have a problem.
The tourist and hotel restaurants will also be open. A lot of nicer restaurants have special Christmas menus for brunch on the 25th & 26th. Once you find a restaurant, check their website for details.
Remember, the 26th is also a holiday so many stores will be closed both days.
I have spent several Christmas holidays in Amsterdam and Haarlem. Amsterdam is still quite lively and it will be fairly easy to find open restaurants. But as mentioned earlier many upmarket restaurants will have special Christmas menu's which are both large and expensive. Haarlem will be much quieter, so if you want to eat there it will be worth booking ahead. Note that on the 31st December and 1 January most restaurants are shut.